Geodesic
On convergence conditions for Dirichlet series on closed polygons
Sbornik. Mathematics, Tome 24 (1974) no. 4, pp. 463-481

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper treats the questions of convergence and summability on a convex polygon $Q$ of the Dirichlet series of a function $f(z)$ which is analytic in $Q$ and continuous on $\overline Q$. Necessary and sufficient conditions for convergence are given for the case of a square; in the general case, if the necessary conditions for convergence are satisfied, it is sufficient that the integral $\int_0^1\frac{\omega(f;t)}t\,dt$ converge. Bibliography: 7 titles. 
@article{SM_1974_24_4_a0,
     author = {V. K. Dzyadyk},
     title = {On convergence conditions for {Dirichlet} series on closed polygons},
     journal = {Sbornik. Mathematics},
     pages = {463--481},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_24_4_a0/}
}
TY  - JOUR
AU  - V. K. Dzyadyk
TI  - On convergence conditions for Dirichlet series on closed polygons
JO  - Sbornik. Mathematics
PY  - 1974
SP  - 463
EP  - 481
VL  - 24
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1974_24_4_a0/
LA  - en
ID  - SM_1974_24_4_a0
ER  - 
%0 Journal Article
%A V. K. Dzyadyk
%T On convergence conditions for Dirichlet series on closed polygons
%J Sbornik. Mathematics
%D 1974
%P 463-481
%V 24
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1974_24_4_a0/
%G en
%F SM_1974_24_4_a0
V. K. Dzyadyk. On convergence conditions for Dirichlet series on closed polygons. Sbornik. Mathematics, Tome 24 (1974) no. 4, pp. 463-481. http://geodesic.mathdoc.fr/item/SM_1974_24_4_a0/